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The Book of Mormon people were taught about Noah the Ark and the flood.

“… these plates of brass, which containthe Holy Scriptures upon them…”     (Alma 37:3) 73 BC
 “… if it were not for the prayers of the righteous, ye would even now be visited with utter destruction; yet it would not be by flood, as were the people in the days of Noah, but it would be by famine, and by pestilence, and the sword…”
(Alma 10:2282 BC
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The ancient pre-Columbus native people had information about Noah, the Ark and the flood.  Even though the Lamanites tried to destroy all of the sacred records. 

 “…I, Mormon… having been commanded of the Lord that I should not suffer the records which had been handed down by our fathers, which were sacred, to fall into the hands of the Lamanites, (for the Lamanites would destroy them) therefore I... hid up in the hill Cumorah all the records which had been entrusted to me by the hand of the Lord, save it were these few plates which I gave unto my son Moroni.”  (Mormon 6:6) 385 AD 

There still remained, among the Aztecs, Maya and Inca, in the 1500’s AD, knowledge and information taught by the Book of Mormon Prophets and recorded upon the "plates of Brass" about the "flood".

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 “…marked with the same [Maya] hieroglyphic of One Flint, the human race suffered a horrible calamity from excessive rains, accompanied with thunder and lighting, which deluged the whole earth, the highest mountains being covered with water caxtolmalictli, which signifies fifteen cubits and that only eight persons excepted from this general calamity in a tlapthipetlacalli, which signifies a house resembling a closed ark, which they represent in their paintings as a little bark with an awning above, over which are eight heads, which are placed there to denote that  from these eight persons the world came re-peopled."    (Antiquities of Mexico, by Lord Edward Kingsborough, Vol. 8 p. 25)  (“Even in the...1840’s”...Kingsborough’s works had not reached America.”) 

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Diego de Landa
 

The Catholic Bishop, Diego de Landa, recorded that the Maya people believed that “four” [men] “escaped when the world was destroyed by the flood.”    (Landa's Relacion, or Relation des choses de Yucatan, by Diego de Landa) A manuscript of the Maya people.
 

Note: "In the selfsame day entered Noah, and Shem, and Ham, and Japheth, the sons of Noah, and Noah’s wife, and the three wives of his sons with them, into the ark;"  (Genesis 7:13)

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Bishop Bartholome de Las Casa, Catholic (1484-1566 AD), was a 16th-century Spanish Bishop.  He became the first resident Bishop of Chiapas.

Bishop Bartholome de Las Casa, recorded that the Maya people already had knowledge about the "flood" as it was recorded in the Bible.

 “…they had among them[the Maya people], information of the flood and the end of the world,... and so they believed that another [event] is about to come which is another...judgment, not of water, but of fire which they say will be the end of the world...." (Catholic Bishop, Bartholome de Las Casas, 1552-1553, Apologetica Historia de las Indias, Cap CCXXXV) 

 

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"Doctor Beatty says, that an Indian in Ohio informed, that one of their traditions was, "Once the waters had overflowed all the land, and drowned all the people then living, except a few, who made a great canoe and were saved."  (The Wonders of Nature and Providence Josiah Priest p. 313)  

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 "The Peruvians were acquainted with the Deluge, and believed that the rainbow was the sign that the earth would not again be destroyed by water.  This is plain from the speech which Mango Capac, the reputed founder of the Peruvian empire, addressed to his companions on beholding the rainbow rising from a hill; which is thus recorded by Balboa in the ninth chapter of the third part of his 'Miscellanca Antarctica' "Mango Capac exclaimed to his companions, 'This is a propitious sign that the world will not be again destroyed by water…'"   (Antiquities of Mexico, by Lord Edward Kingsborough, Vol. 8 p. 25) Note also: (Hubert Howe Bancroft,  The Native Races... published in 1886, P. 16)

Note: "the waters shall no more become a flood to destroy all flesh." "And the bow shall  be in the cloud..." (Genesis 9:15-17)

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    << Francesco Javier Clavijero Echegaray, sometimes referred to as Francesco Saverio Clavigero, 1731-1287, was a Mexican Jesuit teacher, scholar and historian.
He recorded that the pre-Columbian Mesoamerican natives had knowledge and believed the following: 

 "The Chiapanese have been the first peoplers of the New World, if we give credit to their traditions. They say that Votan, the grandson of that respectable old man who built the great ark to save himself and family: from the deluge, and one of those who undertook the building of that lofty edifice which was to reach heaven, went, by express command of the Lord, to people that land."  (The History of Mexico,  1780 AD, By Abbé Francesco Saverio Clavigero V. 1) 

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   "...an old man having foreseen the deluge, [flood], ...built a large canoe...he sent out a raven..."
  "The Mexicans, [Aztecs or Mayas], used to call Noah Coxox,...Teocipactli [or] Tezpi...they use to say that there was once a great deluge, [flood], and that Tezpi, [Noah], in order to save himself from being drowned, embarked in a ship formed like an ark, with his wife, his children and many different animals..."  
 (The History of Mexico, By Abbé Francesco Saverio Clavigero, V. 3, pages 94 & 95) 

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<<Lorenzo Boturini Benaduci was a historian, of New Spain, in North America.

He assembled a vast collection of paintings, maps, manuscripts and native codices. He copied more than 500 pre-Columbian inscriptions.
Boturini recorded that “the historical records of the Amerindians of Mexico, [Mesoamerican native Indians], were among the richest ever assembled by any people in history.  They were accurate, reliable, voluminous, and seemed to confirm every single detail of the biblical narrative, including Genesis, the Flood, the [dispersion], after the destruction of the tower of Babel, and the total solar eclipse that plunged the earth in darkness at the death of Christ.
Boturini
[recorded] that of the many civilizations that had risen and fallen in central Mexico, the Toltecs had independently developed a system of writing, and that by 600 AD the Toltecs had assembled a sacred book recounting the history of their migrations, their laws their customs, and the workings of their calendars.  Boturini suggested that the records of the Toltec were reliable, because Huematzin, the Toltec Moses, drew his information from the...hieroglyphs..."
  
(How to Write the History of the New World: Historys..., By Jorge Cañizares-Esguerra, p. 137-138)